The dynamics of island nucleation and growth —beyond mean-field theory

Fully deterministic calculations of the dynamics of island
nucleation and growth during thin-film deposition are presented,
using a capture zone model that transcends the classical
mean-field approximation. Nucleation rates for various critical
island sizes , 1, 2 are accurately calculated from the
time-dependent monomer density within the capture zones. The
deterministic evolution of the Joint Probability Distribution
(JPD) of island and capture zone size is then calculated. The
JPDs are found to converge rapidly to approximately
scale-invariant forms that are in excellent agreement with Monte
Carlo simulation data.

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